2015 Classes

Here is an overview of our courses from this summer. You can read the class descriptions ("blurbs"), view the global schedule in a grid, or see all the classes sorted by category.

An image of the blurbs describing 2015 Classes

Read the 2015 Blurbs

An image of the grid displaying 2015 Classes

View the 2015 Schedule

Here is the list of classes by subject:

Algebra

  • A (re)Introduction to Polynomials
  • A Dynkin diagram miscellany
  • Abel's Theorem
  • Abelian Groups
  • Abstract Nonsense
  • Advanced Linear Algebra
  • Braid Groups
  • Burnside's Lemma
  • Category Theory in Sets
  • Cyclotomic Polynomials and Extensions
  • Extensions
  • Finite Fields
  • Galois Theory
  • Introduction to Groups
  • Laurent Phenomenon
  • Lie Algebras
  • Linear Algebra
  • Primitive roots
  • Reflection Groups
  • Representation Theory of Finite Groups
  • Ring Theory
  • Sylow Theorems
  • The Banach–Tarski Paradox
  • The tale of summation is in order!
  • Tiling Problems
  • Tropical Curves
  • Colloquium: Putting the Algebra in Algebraic Topology

Analysis

  • Almost All You Want
  • Differentials and higher differentials
  • Differentiation under the Integral Sign
  • Functions of a Complex Variable
  • Fundamental Theorem of Calculus in Dimension n
  • Infinitesimals
  • Lebesgue Measure
  • Metric Spaces
  • Multivariable Calculus
  • Normal Numbers
  • The Ham Sandwich Theorem and Friends
  • What's Up With e?
  • Colloquium: Cauchy's functional equation

Applied Math

  • A Card Trick, and a Set
  • A Mathematician Goes to Vegas
  • Building a machine that learns like a human
  • Cosine Waves on Musical Staves
  • From Geometric Optics to High Speed Underwater Photography
  • Group operations' harmonic implications
  • Mathematical Magic
  • Optimization Problems on Graphs
  • Quantum factoring
  • Special Relativity
  • Statistical Modelling
  • The Cake is a Lie
  • The Fast More Four Do Over
  • The Hidden Dance of Partial Differential Equations
  • The mathematics of polygamy (and bankruptcy)
  • Time-Frequency Analysis
  • Unsolved Problems in Cosmology
  • Voting Theory
  • Colloquium: An Intro to "Data Science"
  • Colloquium: Pad Thai with Electrons
  • Colloquium: Secure Genomic Computation: a Contest

Combinatorics

  • Coloring Maps
  • Combinatorial Game Theory
  • From Counting to a Theorem of Fermat
  • Generating Functions, Catalan Numbers, and Partitions
  • Graphs on Surfaces
  • Induced Matchings from Szemeredi's Regularity Lemma
  • Intro Knot Theory
  • Knight's Tours
  • Latin Squares
  • Posets
  • Qualifying Quiz Problem 6
  • Summing Series
  • The Hoffmann Singleton Theorem
  • The Pruefer Correspondence
  • The Robinson-Schensted Correspondence
  • The Tower of Hanoi
  • Tower of Hanoi
  • Unlikely Maths
  • Wagner's Theorem
  • Colloquium: Triples

Computer Science

  • Algorithms
  • Automated Proofs in Geometry
  • Cryptography
  • Cryptography: What is it and Why Do we Care?
  • Error-Correcting Codes
  • Introduction to Complexity
  • Learn to code!
  • Many Facets of Optimization
  • P vs NP
  • Colloquium: Computers: Friends or foes of the modern mathematician?

Geometry

  • Aperiodic Tiling
  • Apollonian Circle Packings
  • Classifying Symmetry
  • Coloring in Space
  • Counting the Faces of Cut-Up Spaces
  • DIY Hyperbolic Geometry
  • Elliptic Curves Day 1
  • Fractal dimensions
  • Non-classical Constructions
  • Quaternions and rotations
  • Quaternions and rotations
  • Shortest Distance
  • The Projective Plane
  • Colloquium: Can You Hear the Shape of a Drum?
  • Colloquium: Neural Codes
  • Colloquium: Polyhedral Symmetry in the Plane?

History, Literature, and Education

  • Bad History: A Crash Course in Historiography and how not to do the History of Math
  • Development of Probability
  • History of Math
  • The History of Calculus
  • Turing and his Work
  • Colloquium: Are We Special?
  • Colloquium: Finding my Place in {Teacher Educators} ∩ {Mathematicians}: Bringing a Mathematical Eye to Teacher Education

Logic/Set Theory

  • A game you can't play (but would win if you could)
  • Exploring Equality via Homotopy and Proof Assistants
  • Fun with Compactness in Logic
  • LARGE cardinals!
  • Martin's Axiom and Ramsey Ultrafilters
  • Mathcamp Crash Course
  • Measure and Martin's Axiom
  • Ordinal Arithmetic
  • Stupid Games on Uncountable Sets
  • The Löwenheim-Skolem Theorem
  • Ultrafilters
  • Colloquium: Hydras
  • Colloquium: Making Cantor Super Proud

Number Theory

  • Absolute Values: All the Other Ones
  • Algorithms in Number Theory
  • Continued Fractions
  • Multiplicative Functions
  • Quadratic Reciprocity
  • The Factorial Function
  • pNumber Theory
  • Colloquium: My Favorite Prime

Probability/Statistics

  • Markov Chains to Support your Probabilistic Exploits

Problem Solving

  • Problem Solving: Combinatorics
  • Problem Solving: Inequalities
  • Problem Solving: Linear Algebra
  • Problem Solving: Tetrahedra
  • Rapid Fire Problem Solving

Topology

  • Classifying Spaces
  • Combinatorial Topology
  • Fundamental Group
  • Galois Cohomology
  • Homotopy Theory
  • Point-set Topology
  • Colloquium: Reeb Foliation of the 3-Sphere